Exponential and Logarithmic Functions

The video tutorial covers solving equations using logarithms, exponential growth and decay problems, depreciation and appreciation calculations, compound interest, and inverse functions. It provides step-by-step instructions and encourages students to practice independently.

What is the solution for x in the equation 4 * 2^(2x) - 3 = 60 using logarithms?

• x = 1.989

• x = 2.0

• x = 2.5

• x = 1.5

How can you solve the equation 13^(2x) = 84 using logarithms?

• x = 1.2345

• x = 1.6789

• x = 0.5678

• x = 0.8637

If a population grows by 7.4% per year, how many years will it take to reach 60,000 from 25,000?

• 8 years

• 15 years

• 12.3 years

• 10 years

A car worth $18,000 depreciates at 13% per year. What will its value be in 7 years?

• $6,791

• $10,000

• $8,000

• $5,000

What is the future value of a $2,000 ring appreciating at 2.5% annually over 20 years?

• $3,277.23

• $4,000

• $3,000

• $2,500

Which equation models $800 invested at 5% interest compounded quarterly?

• A = 800(1.05)^t

• A = 800(1.0125)^(4t)

• A = 800(1.0125)^t

• A = 800(1.05)^(4t)

How do you convert an annual interest rate of 7.2% to a monthly rate?

• 0.5%

• 0.7%

• 0.6%

• 0.581%

What is the inverse function of f(x) = 4^x?

• g(x) = log(x)

• g(x) = x^4

• g(x) = 4^x

• g(x) = log_4(x)

How do you express 3^x = 1/81 in logarithmic form?

• log_3(x) = 81

• log_3(81) = 4

• log_3(1/81) = -4

• log_3(1/81) = 4

What is the base of the logarithm in the equation 4^x = y?

• 10

• y

• x

• 4